I agree with Old Fat Bald Guy, on the Clutch rating. Should not be visible, but the manager would just have to judge by looking at the long-term record.

Proneness to injury, would also be evaluated over time. Newly captured slaves will probably not be carrying their medical records with them. This would also have to be observed over time by a medical file kept by the game.

More stats would be a good thing. Championship Manager has lots of stats available which look difficult to judge, i.e. Decisions, Creativity, Determination, Pressure, Professionalism, Morale,
Current Playing Form,

Other stats look to be part of Coliseum's Ratings, i.e. Anticipation, Balance, Aggression, Finishing,
Pace (top speed), Positioning, Stamina, Strength, Technique, Work Rate, Agility, Reflexes, Condition. These are some of CM's invisible attributes: Adaptability, Consistency, Versatility, Important Matches, Injury Proneness, Loyalty, Pressure, Professionalism, Temperament, Vision. Maybe some of the current numbers could be sub-divided into additional stats.

These stats from CM could also be nice:
Flair = The gladiator automatically generates more attendance
Dirtyness = Generates more kills. But may also provoke a better performance from wary opponents.
Height / Weight = Height would give someone a slight reach advantage and greater weight could slightly absorb blows better.

For training during the season, it does not seem like the manager is nearly as capable as other hired trainers. My manager had good stats but my main fighter did not progress in stats. Maybe we could hire a training staff for better training results.